1. Field of Invention
The present invention relates to a surface interferometry and more particularly to a variable near-null compensator and a figure metrology apparatus for measuring aspheric surfaces by subaperture stitching interferometry and measuring method thereof.
2. Description of Related Arts
Optical aspheres are widely used in modern optical systems such as telescopes, lithographic objectives and so on. Due to the increase of the requirements for the performances of the modern optical systems, the aspheric surfaces with large caliber and high accuracy become major features in modern optical system. The deviation of the surface figure for an aspheric surface is typically measured by an interferometer. However, the interference fringes on large caliber aspheric surfaces are too dense to be resolved owning to the departure of large aspheric surfaces which can't be tested within the vertically measuring range of the wavefront interferometer. In order to completely resolve the interference fringes on large caliber aspheric surfaces, a compensator is adapted to reshape the spherical test wavefront to match the test aspheric wavefront. The compensator is required to compensate almost all of the aberrations, and as a result, the residuals aberrations have to be less than 1/100 waves PV (peak-to-valley). Therefore, if the shape of the aspheric surface generates a slight change, the structure of the compensator usually is required to be re-designed. In other words, one type of compensator only can be used for a certain type of aspheric surface. Furthermore, the convex aspheric surface reflectors which are used as secondary mirrors in telescopes usually comprise a compensator with aspheric surfaces, in such manner that, the manufacturing cost and complexity of such telescopes are higher. Due to the limitations of the materials and the manufacturing accuracy of the compensator, it is generally not suitable for large-caliber aspheric surfaces reflector.
China Patent Number, CN101251435A, entitled as “Subaperture Stitching Workstation for Large Optical Surfaces”, discloses a subaperture stitching workstation composed of an interferometer, a five degree-of-freedom adjustment platform for the interferometer, and a tip-tilt platform for the test mirror. The workstation is mainly applied to the subaperture measurement for large optical surfaces. The subaperture stitching interferometry is adapted by the workstation. A series of mutually overlapping subapertures located at different positions on the test mirror are measured one by one and provide a surface figure deviation of the full aperture by the subasperture stitching algorithm. No null optics, such as compensator, is required and mild-slope of aspheric surfaces (which has a lower slope of asphericity) are able to be measured directly so as to extend measurable apertures thereof. However, subapertures are required to cover the full aperture of the aspheric test mirror and the asphericity of each subaperture must be reduced to be small enough to ensure that the departure of such aspheric test mirror is within the vertically measuring range of the interferometer, so that the interference fringes can be easily resolved by the interferometer. Therefore, this method is not applicable to high-slope aspheric surfaces (which has a higher slope of asphericity). Otherwise, the large aperture aspheric surfaces must be divided into hundreds of subapertures so as to sufficiently reduce the departure of the subapertures thereof, such that the problem of the environmental disturbance and lower measurement repeatability are generated. As demonstrated by inventors, Chen and Dai, in the “Calculation of subaperture aspheric departure in lattice design for subaperture stitching interferometry” (Optical Engineering, vol. 49/2 (2010) pp. 023601-1˜5), up to 142 subapertures may be required to test a 360 mm aperture convex aspheric surface with a 4-inch subaperture interferometer.
To effectively reduce the number of subapertures and the complexity of the measurement, a near-null compensator can be introduced to the subaperture stitching interferometry, wherein the near-null compensator is different from conventional null compensator. The near-null compensator is required to compensate most of the aberrations of subaperures such that the residual aberrations reduced within the vertically measuring range of a standard interferometer (for example, 10 waves PV). However, different subapertures located at different positions on aspheric surfaces will generate different ranges of aberrations, so that the near-null compensator is required to be adjustable to match the different ranges of aberrations.
China Patent CN1587950A, entitled as “An interferometric method for aspheric surface metrology using partial compensation lens”, discloses a compensator having refractive lens for partially compensating the departure of aspheric surfaces. It is not applicable to off-axis subapertures on the aspheric surfaces. Moreover the compensator can't be adjusted to compensate the different ranges of aberrations.
China Patent CN1746648A, entitled as “A test system for large steep aspheric surfaces”, discloses a compensator having partially compensating lens which is used to test annular subapertures. In this manner, the large aperture and high-slope aspheric surface with large amount of annular subapertures can be tested. However, the method also can not be applicable to off-axis subapertures on the aspheric surfaces, but it is applicable to rotationally symmetric concave aspheric surfaces.
In addition, United States Patent Publication No. 2009/0251702 A1 published on Oct. 8, 2009, provided by the inventors, Murphy, Devries, Brophy and Forbes, entitled as “Stitching of near-nulled subaperture measurements”, and the reference document entitled as “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null” (CIRP Annals-Manufacturing Technology, vol. 59/3 (2010), pp. 547-550) provided by QED Technologies Inc., suggest a metrology system and method for measuring aspheric surfaces by subaperture stitching. The method discloses a variable near-null compensator comprising a pair of Risley prism which is mutually counter-rotating to generate variable amounts of coma and astigmatism. In other words, the pair of Risley prisms can be tilted to compensate most of the subaperture aberrations. Hence, the variable near-null compensator can be adjusted to compensate most of the aberrations. The shortcoming of the above mentioned method is that the need of adjustment the counter-rotating and tilting angles so as to tight the accuracy of the mechanical alignment. Moreover, the spaces between the interferometer and the test mirror surface need to be reserved under the overall tilt (probably up to 40 degrees) so as to generate the hassle for arranging the testing optical path.
According to a document published by Acosta and Bard (Acosta E., et al., “Variable aberration generators using rotate Zernike plates”, J. Opt. Soc. Am. A, vol. 22/9 (2005), pp. 1993-1996), variable amounts of pure Zernike modes can be generated by rotating a pair of Zernike phase plates, which can be used to calibrate ocular aberrometers. This idea has not been realized for optical figure metrology because the aberration of the aspheric surfaces requires to be completely compensated. Different aspheric surfaces require different types of compensators or computer-generated holograms (CGHs) with different phase functions so that only one CGH phase plate is required to compensate a single-fixed aberration. Utilizing a pair of CGH plates generates the problems of the increase of disturbance orders of diffraction, and reduces efficiency of diffraction. The problems as mentioned above must be carefully solved by other techniques. Besides, when using a pair of counter-rotating phase plates for optical figure metrology, the method for designing the phase function is different from conventional CGH design. However, the conventional CGH design is based on a single-fixed phase, wherein the phase function of the conventional CGH design is determined by the difference of the aspheric wavefront propagating to the phase plate and the emerging wavefront expected to converge to an ideal image point. While using a pair of phase plates, the phase function is not well defined by the aspheric and emerging wavefronts because the phase plates do not completely compensate the aberrations of all subapertures. The phase plates have to compensate most of aberrations of different subapertures located at different positions on aspheric surface with different slopes. Therefore, a new CGH design method is required for defining the phase function.